Get rid of the shaking noise/motion the carts make when pushed quickly. Need new wheels to do this?

If we can't get rid of the shaking, add some kind of material to dampen the noise the carts make when they do shake.

Automatic detection of trash on shelves. This would probably be prohibitively expensive for little gain, but pretty cool to do. Set up video cameras (or some other type of sensor? Weight sensor maybe?) that observe the empty space on the sides of shelves. Whenever an object is detected as sitting in that space, we would know that trash is located there, and to go pick it up.

Automatic floor cleaning! Get a squad of iRobot Roombas to run overnight when the library is closed and sweep all the floors.

Electronic timers that employees can push to time how long it takes to complete a task. Basically a big red button that we press before we start a task that counts how long it takes to complete the task.

Automatic chair push-in-ing. Program the Roombas (or similar devices) to search for chairs in the library (use RFID emitter tags on the chairs?) , and attempt to scoot them in under the tables/study cubbies overnight.

Scan out-of-copyright books to contribute to Project Gutenberg/similar. Try to digitize information from statistical books and submit that data to public databases?